Boundary blow-up insemilinear elliptic problems with singular weights at the boundary

Abstract

In this paper, we study under what conditions on m(x) and f(u) the problem Δu=m(x)f(u) has a solution in a bounded domain D, which tends to infinity, as x tends to the boundary. We show that if m(x) is singular at the boundary of D, except that the Keller-Osserman condition must hold, the growth of f at the infinity has to be slow for a solution to exist. Some existence results have been established.